Title Improved hanger design for robustness of through-arch … · 2016-06-05 · bracings, the...

Title Improved hanger design for robustness of through-arch bridges

Author(s) Jiang, R; Au, FTK; Wu, QM

Citation Proceedings of the ICE - Bridge Engineering, 2013, v. 166 n. BE3,p. 193-204

Issued Date 2013

URL http://hdl.handle.net/10722/202697

RightsPermission is granted by ICE Publishing to print one copy forpersonal use. Any other use of these PDF files is subject toreprint fees

Improved hanger design forrobustness of through-arch bridges

&1 Rui-Juan Jiang BEng, MEng, PhDSenior Engineer, The Research Centre, Shenzhen Municipal EngineeringDesign and Research Institute, Shenzhen, China; The School of Civil

Engineering, Shandong University, Jinan, Shandong, China;

Department of Civil Engineering, The University of Hong Kong, HongKong, China

&2 Francis Tat Kwong Au BSc(Eng), MSc(Eng), PhD, MICE, FIStruct-E,FHKIE, CEngProfessor, Department of Civil Engineering, The University of HongKong, Hong Kong, China

&3 Qi-Ming Wu BEng, MEngEngineer, The Research Centre, Shenzhen Municipal EngineeringDesign and Research Institute, Shenzhen, China

1 2 3

Hangers in through-arch bridges are important components since they suspend the entire bridge deck from the arch

ribs. Local damage at a hanger may lead to subsequent damage of various components in the vicinity or even

progressive collapse of the bridge. After reviewing the conventional design of double-hangers in through-arch

bridges, this paper puts forward a new design approach. The suitability and robustness of this new approach are then

verified by numerical simulation of a real bridge. The impact effects induced by local fracture of a hanger on the other

structural members are then simulated by dynamic time–history analyses. The new approach of hanger design is

shown to improve the structural robustness. In particular, when one or more hangers are damaged thereby causing

local failure, the through-arch bridge will not be endangered and will still maintain reasonable overall load-carrying

capacity so that the necessary emergency measures can be taken.

NotationRd structural response under dead load

Ri structural response under hanger fracture

dt duration of hanger fracture

g impact coefficient due to hanger fracture

1. IntroductionA progressive collapse is a structural failure that is initiated by

localised structural damage and subsequently develops, as a

chain reaction, into a failure that involves a major portion of

the structural system (Ellingwood and Dusenberry, 2005). The

main feature of progressive collapse is that the total

cumulative damage is disproportionate to the original cause

(General Services Administration, 2003; Vlassis et al., 2006).

It often means injury to people, damage to the environment or

economic losses for the society. The progressive collapse of

the Ronan Point Apartment Tower in Canning Town,

London, UK in May 1968 illustrated a lack of provisions

for general structural integrity or robustness in existing

building codes. It also prompted efforts to enhance structural

robustness in design codes in various countries (Pearson and

Delatte, 2005).

As it is not feasible to foresee all possible sources of collapse

initiation, a rational design approach to guard against

progressive collapse should aim at controlling the conse-

quences of local damage rather than just attempting to prevent

damage on the whole. This can be achieved through structural

robustness, which is related to the concept of progressive

collapse. In EN199 1-1-7 Eurocode 1: Part 1-7 Accidental

Actions (CEN, 2006), structural robustness is defined as ‘the

ability of a structure to withstand events like fire, explosions,

impact or consequences of human error without being

damaged to an extent disproportionate to the original cause’.

There are various practical ways to achieve a robust structure,

including an approach based on energy absorption (Beeby,

1999), an algorithm based on energy ratio (Smith, 2003) and so

on. Others have found that robustness depends on a number of

structural parameters, including strength of members and

connections, ductility, energy absorption, provision of alter-

native load paths and resistance to fire and corrosion (Agarwal

Bridge EngineeringVolume 166 Issue BE3

Improved hanger design for robustness ofthrough-arch bridgesJiang, Au and Wu

Proceedings of the Institution of Civil Engineers

Bridge Engineering 166 September 2013 Issue BE3

Pages 193–204 http://dx.doi.org/10.1680/bren.11.00025

Paper 1100025

Received 28/04/2011 Accepted 12/10/2011

Published online 04/04/2013

Keywords: bridges/cables & tendons/failures

ice | proceedings ICE Publishing: All rights reserved

193

et al., 2006; Alexander, 2004; IStructE, 2002). Jiang and Chen

(2008) also carried out a review on the progressive collapse and

control design of building structures. According to Eurocode 1,

the principle is that local damage is acceptable, provided that it

will not endanger the structure and that the overall load-

carrying capacity is maintained during an appropriate length

of time to allow the necessary emergency measures to be taken

(Gulvanessian and Vrouwenvelder, 2006).

Hangers in through-arch bridges are important components

since they suspend the entire bridge deck from the arch ribs.

Local damage at a hanger may lead to subsequent damage of

various components in the vicinity or even progressive collapse

of the bridge. Real-time monitoring and diagnoses of the

health condition of hangers have been conducted (Li et al.,

2007), although the state of the art is not yet fully reliable (Li

et al., 2008). After reviewing the conventional design of

double-hangers in through-arch bridges, this paper puts

forward a new design approach. The suitability and robustness

of this new approach will then be verified by numerical

simulation of a real bridge.

2. Conventional design of arch bridgehangers

Each hanger of a through-arch bridge is anchored to the arch

rib at one end and a transverse beam at the other. The double-

hanger anchorage (Figure 1) is often adopted instead of the

single-hanger anchorage for convenience of hanger replace-

ment. The two vertical hangers at the same anchorage are

conventionally designed to be identical both in material and

cross-section. As they are subject to approximately the same

stress levels and variations as well as corrosive environment,

they approach the end of their service lives at roughly the same

time. When the slightly weaker hanger in the pair fails first, the

resulting impact and hence overstress induced in the adjacent

hanger will likely cause its immediate failure, damage other

structural members in the vicinity and possibly lead to

progressive collapse. Therefore in these circumstances, the

conventional design method improves neither the safety nor

the convenience of hanger replacement.

3. Improved design of arch bridge hangers

To avoid the fracture of a hanger triggering the failure of

another in the same group, it is desirable for hangers in the

same group to be designed with different service lives. It is

feasible to provide hangers of the same material but with

different cross-sectional areas (Figure 2). With the use of

different cross-sectional areas and appropriate control of initial

hanger tension by proper jacking during erection, hangers in

the same group will have different stress levels in spite of

similar stress ranges subsequently, and therefore different

service lives. The hanger with larger cross-section and lower

stress level is expected to keep the arch bridge safe when the

other hanger with smaller cross-section and higher stress level

fails unexpectedly. The performance of this new design method

will be studied numerically using a through-type arch bridge,

namely Shenzhen North Railway Station Bridge, using the

commercial software ANSYS (2010).

Two identical hangers

Bridge deck

Longitudinal girder Transverse girder

Figure 1. Conventional double-hanger anchorage with two

identical hangers

Two different hangers

Longitudinal girderTransverse girder

Bridge deck

Figure 2. Improved double-hanger anchorage with two different

hangers

Double-hanger

Arch rib

West

Arch rib

East8

Railway tracks150

Figure 3. Elevation of the bridge analysed (unit: m)


Improved hanger design forrobustness of through-archbridgesJiang, Au and Wu

194

4. Modelling of the chosen bridge

Shenzhen North Railway Station Bridge (Figure 3) in South

China is a through-type tied arch bridge, which was built in

2000, spanning 150 m over a total of 29 railway tracks. The

bridge has a span-rise ratio of 4?5. The width of deck is 23?5 m.

Horizontal cables are installed in the longitudinal steel box

girders of the deck to provide the necessary tie forces. The

bridge has two vertical arch ribs tied to the piers and each rib is

composed of four concrete-filled steel tubes having a lattice

girder section of 2?0 m in width and 3?0 m in height (Figure 4).

There are 17 conventional vertical double-hanger anchorages

for each arch rib at spacing of 8?0 m. The spacing between

hangers in each anchorage is 0?48 m. The composite bridge

deck consists of concrete slabs supported on a steel grid

comprising two longitudinal steel girders and 17 transverse

steel girders. The material properties of the bridge are listed in

Table 1. More details about this bridge are found in Li et al.

(2002). The bridge has been providing satisfactory service so

far. Figure 5 shows the three-dimensional (3D) finite-element

model developed using the commercial package ANSYS.

The concrete-filled steel tubes are modelled by the regular 3D

Euler–Bernoulli beam elements BEAM4 with equivalent cross-

sectional and material properties, namely cross-sectional area of

0?58 m2, modulus of elasticity of 34?5 GPa, moment of inertia of

0?02495 m4, torsional moment of inertia of 0?04816 m4,

Poisson’s ratio of 0?2 and density of 2160?55 kg/m3. The

BEAM4 elements are also adopted to model the arch rib

bracings, the longitudinal steel box girders, the steel tubes

connecting the four concrete-filled steel tubes of each arch rib.

The transverse steel girders of the bridge deck are modelled

using the 3D Timoshenko beam elements BEAM188, which are

provided with an additional degree of freedom at each node to

cope with warping. The concrete slabs of the bridge deck are

modelled as equivalent planar space frames by grillage analogy

using BEAM4 elements. The hangers are modelled by the 3D

spar elements LINK8 that can take axial forces only. The cross-

sectional properties of these components, except those of the

transverse girders, are listed in Table 2. The BEAM188 element

of ANSYS needs the cross-section shape and dimensions as

input information for automatic calculations. The connections

between the longitudinal box girders and transverse girders, and

between the concrete slabs and all steel girders (Figure 5) are all

regarded as rigid connections and modelled by the multipoint

constraint elements MPC184. There are 4672 elements and 2448

nodes in total in this 3D finite-element model. In this bridge, the

arches are fixed rigidly to the piers, which are effectively tied

together by horizontal cables. Since the boundary conditions of

the arch ribs above the piers have negligible effect on dynamic

analysis by this 3D finite-element model, the ends of the arch

ribs can be treated as effectively fixed in all degrees of freedom,

while the horizontal cables are ignored. The two longitudinal

steel box girders are supported on transverse beams located at

the piers. For convenience, the anchorages of each arch rib are

numbered from 1 to 17 from west to east. The two hangers at

each anchorage are numbered as a and b for the north arch rib,

and a9 and b9 for the south arch rib (Figure 6). The baseline

finite-element model is developed by adjusting the initial lengths

and forces of hangers by iteration so that the bridge geometry

under permanent loading agrees with that shown on the

illustrations.

5. Impact effect due to hanger fracture

Consider a double-hanger anchorage comprising two identical

hangers. In case one of the hangers fractures, simplified static

analysis predicts that the other hanger will have its tensile

stress doubled. However, rigorous dynamic analysis predicts

Concrete-filled steel tube(CFST) of nominal

diameter 750 1250

Upper outerCFST

Steel tubes

Lower outer CFSTLower inner CFST

Upper inner CFST

Brid

ge c

entre

line

on th

is s

ide

2250

Figure 4. Cross-section of an arch rib (unit: mm)

Material

Modulus of

elasticity: GPa

Coefficient of

expansion: 61025

Poisson’s

ratio

Shear modulus:

GPa

Density:

kg/m3 Yield stress: MPa

Concrete 34?5 1?0 0?2 14?375 2500 —

Steel 206 1?2 0?3 79?231 7850 340

Hanger 205 1?2 0?3 78?846 7850 1670 or 1860

Table 1. Material properties of the bridge analysed



195

the stress in the other hanger to over-shoot beyond the

increased static stress value and oscillate for a while before

becoming steady again. If this maximum stress in the other

hanger due to transient impact effects is high enough to

fracture this hanger, it may cause progress failure of the whole

structure. To ensure the robustness of an arch bridge, one

should first assess the impact effect caused by sudden hanger

fracture on components in the vicinity and the remaining

structure. To simulate the sudden fracture of a hanger, the

member is omitted from the model and replaced by the steady

internal forces in service there (Figure 7), which are then

assumed to decrease linearly to zero within a duration dt as

described in Section 5.1. The impact effect due to hanger

fracture is studied by carrying out dynamic analysis using the

3D finite-element model. The time step for dynamic analysis is

taken as 0?05dt within the duration of hanger fracture and

0?01 s thereafter. For convenience, Rayleigh damping (Bathe,

1996) is assumed with the damping ratio taken as 0?02. The

impact coefficient g is defined as

1. H~ RdzRið Þ=Rd

where Rd is the structural response under dead load and Ri is

the maximum structural response owing to hanger fracture

only. The structural response of the bridge may take the form

of stresses, bending moments, axial forces, displacements and

so on. The contribution of vehicular live load to the structural

response is ignored in comparison with the more significant

dead load effects.

5.1 Appropriate value for duration of hanger

fracture dt

In order to determine the appropriate value for the duration

of hanger fracture dt for the subsequent analyses, the

relationship between the impact coefficient g and the duration

of hanger fracture dt was studied. In view of symmetry,

anchorages 1 to 9 were chosen for further analysis. At each of

the anchorages, it was assumed that fracture occurred to one

of the hangers in the group within different values of duration

of hanger fracture dt, and the impact coefficient g of the other

hanger in the group was evaluated from dynamic analysis.

The relationship between impact coefficient g and duration of

hanger fracture dt is plotted in Figure 8 for the fracture of

selected hangers, including the shortest hanger 1a, the second

shortest hanger 1b, the medium length hanger 5a and the

longest hanger 9a.

Figure 8 shows that all g–dt curves have essentially the same

trend. In general, the impact effect due to hanger fracture

increases when the duration of hanger fracture dt decreases, but

it tends to stabilise when dt becomes 0?01 s or smaller. In other

words, convergent results of impact can be obtained if a value

of dt not exceeding 0?01 s is chosen. Therefore in the

subsequent analyses, dt is taken as 0?001 s. When dt exceeds

1?0 s, it also tends to decrease to a relatively stable value as the

slow action can be regarded as largely static in nature. In

Components

Cross-sectional area:

61023 m2

In-plane moment of

inertia: 61023 m4

Out-of-plane

moment of inertia:

61023 m4

Torsional moment of

inertia : 61023 m4

Longitudinal girder 32?00 2?1010 4?607 4?500

Horizontal connecting tube 12?25 0?2331 0?2331 0?4662

Vertical connecting tube 7?383 0?0511 0?0511 0?1021

Inclined connecting tube 7?383 0?0511 0?0511 0?1021

Horizontal bracing tube 15?39 0?4622 0?4622 0?9244

Inner bracing tube 7?314 0?0775 0?0775 0?1549

Longitudinal grillage member of slab 639?7 11?610 32?02 19?96

Transverse grillage member of slab 480?0 9?2710 9?271 21?58

Hanger 2?348 — — —

Table 2. Cross-sectional properties of components in the bridge

analysed

Double-hangerArch rib

Transverse girderLongitudinal girder

Concrete slab

Figure 5. Finite-element model of the bridge analysed



196

particular, Figure 8 shows the impact coefficients at the

surviving hangers 1b, 1a, 5b and 9b when each of hangers

1a, 1b, 5a and 9a is fractured respectively, and the correspond-

ing maximum impact coefficients are 1?71, 1?63, 1?45 and 1?42.

One may therefore conclude in general that, the shorter the

hanger group is, the higher is the impact effect. One may next

focus on the group comprising the shortest hanger 1a and

second shortest hanger 1b. The impact effect (g 5 1?71) on 1a

induced by the fracture of hanger 1b is higher than that (g 5

1?63) on 1b induced by the fracture of hanger 1a, as hanger 1a

is shorter than hanger 1b. Hence at the same anchorage, the

longer hanger should be designed with a longer service life

compared to the shorter one.

5.2 Impact effect on various members owing to

hanger fracture

The fracture of hanger 1b of the north rib was chosen for

further study to identify the impact effects on other structural

components. The impact coefficients of the other hangers in

the north and south ribs are shown in Figures 9 and 10

respectively. They confirm that the impact effects are mainly

experienced by hangers in the vicinity of 1b with a maximum

impact coefficient of 1?70 experienced by hanger 1a, while

those under the opposite rib are hardly affected. Figures 11

and 12 show the maximum impact coefficients of the upper-

outer concrete-filled steel tubes (Figure 4) in the north and

south ribs respectively. They also confirm that the impact

effects are confined to the parts of north rib in the vicinity and

that the effects are quite mild with a maximum impact

Simulation of hanger fracture

Figure 7. Simulation of hanger fracture

1a 1b

1a’ 1b’ 5a’ 5b’ 9a’ 9b’ 13a’ 13b’ 17a’ 17b’

... ... ... 5a 5b 9a 9b

North rib

South rib

... ... ... ...... ...13a 13b 17a 17b.. ......

... ... ... ... ... ... ... ... ... ... ... ...

Figure 6. Numbering of hangers in north and south ribs

1.8

1.7

1.6

1.5

1.4

1.3–5.0 –4.0 –3.0

Log ( )–2.0 –1.0 0.0 1.0

1a1b5a9a

Impa

ct c

oeffi

cent

=0.0001 s =0.001 s =0.01 s =0.1 s =1 s

Figure 8. Relationship between impact coefficient and duration of

hanger fracture



197

coefficient of 1?07, while the south rib is hardly affected. The

conclusion drawn is that the remaining hanger paired with a

fractured hanger suffers the major part of the impact effect,

while the effects on the other parts of the structure are

minimal. Therefore the hangers should be so designed to avoid

successive damage should any hanger happen to fracture.

When the hangers at a certain anchorage happen to fracture,

the support conditions of the longitudinal girders will be

affected. To assess the behaviour of the longitudinal girders

when hanger 1b fractures, the maximum normal stresses of the

north and south longitudinal girders of the bridge are

calculated and shown in Figures 13 and 14 respectively. It is

noted that the maximum normal stress levels of the two

longitudinal girders under service loading are around 20 MPa,

which are far below the allowable stress of 210 MPa. However,

when hanger 1b happens to fracture, the most affected part of

longitudinal girder in the vicinity has maximum normal stress

exceeding 40 MPa, although it is still much lower than the

allowable stress. Obviously when both hangers at the same

anchorage fracture at the same time, the longitudinal girder

will be significantly affected as the load path is substantially

altered. In the original structure, the bridge deck is primarily

supported by the transverse girders which are suspended from

the hangers. Once a group of hangers is fractured, the

corresponding transverse girder will then be carried by the

longitudinal girder, thereby inducing substantial bending in it.

The other parts of the longitudinal girder further away from

the damage and the opposite longitudinal girder are also

hardly affected.

6. Robustness study of conventional andimproved designs

In order to demonstrate the robustness of the new improved

hanger design method, a comparison is carried out using the

same bridge. According to the original design, each hanger of

the bridge is composed of 61 parallel prestressing steel wires

of 7 mm diameter (i.e. 61-W7), with characteristic tensile

strength of 1670 MPa and a total cross-sectional area of

2348 mm2. The design code for highway cable-stayed bridges

2.50

1.7022.00

1.50

1.00

0.50

0.00

1a 2a 2b 3a 3b 4a 4b 5a 5b 6a 6b 7a 7b 8a 8b 9a

Hanger number

9b 10a10

b11

a11

b12

a12

b13

a13

b14

a14

b15

a15

b16

a16

b17

a

Impa

ct c

oeffi

cien

t

Figure 9. Impact coefficients of hangers in north rib when hanger

1b fractures

2.50

1.052

2.00

1.50

1.00

0.50

0.00

1a′1b

′2a

′2b

′3a

′3b

′4a

′4b

′5a

′5b

′6a

′6b

′7a

′7b

′8a

′8b

′9a

′

Hanger number

9b′10

a′10

b′11

a′11

b′12

a′12

b′13

a′13

b′14

a′14

b′15

a′15

b′16

a′16

b′17

a′17

b′

Impa

ct c

oeffi

cien

t

Figure 10. Impact coefficients of hangers in south rib when hanger

1b fractures



198

in China (MTPRC, 2007) specifies the factors of safety

for permanent and temporary situations to be 2?5 and

2?0 respectively for prestressing steel wires and strands.

Therefore the allowable stresses of the prestressing steel wires

are 668 MPa and 835 MPa for permanent and temporary

situations respectively.

Based on the new method of robust hanger design put forward

in this paper, the two hangers at the same anchorage are

designed differently while maintaining roughly the same total

cross-sectional area using 7-wire strands which are more

commonly available on the market. The smaller hanger

comprises 13 7-wire strands spun from 5 mm prestressing steel

wires (i.e. 13-7W5) with a total cross-sectional area of 1787 mm2,

while the bigger one is made of 20-7W5 prestressing steel strands

with a total cross-sectional area of 2749 mm2. The characteristic

tensile strength of prestressing steel strands is 1860 MPa. Using

the same factors of safety (MTPRC, 2007), the allowable

stresses are 744 MPa and 930 MPa, respectively, for permanent

and temporary situations. While the total cross-sectional area of

the group of hangers of 4536 mm2 in the improved design is

smaller than 4696 mm2 in the original design, this is more than

offset by the higher characteristic tensile strength of prestressing

steel strands. Each anchorage of the improved hanger design is

to carry the same total tensile force as in the original design,

except that the ratio of stress in the smaller hanger to that in the

bigger hanger due to permanent loading is controlled to be

approximately 2?0 by proper jacking during erection of the

bridge. The maximum stresses in the hangers of the improved

design due to all expected loading are also checked to ensure that

the necessary factors of safety are provided. The baseline finite-

element model of the bridge with the improved hanger design is

similarly developed to achieve the required bridge geometry

under permanent loading.

50 x coordinates of north arch rib: m

75 100 125 1502500.90

0.95

1.00

1.05

1.10

1.15

1.20

Impa

ct c

oeffi

cien

t

Figure 11. Impact coefficients of upper-outer tube in north rib

when hanger 1b fractures

50

x coordinates of north arch rib: m

75 100 125 1502500.90

0.95

1.00

1.05

1.10

1.15

1.20

Impa

ct c

oeffi

cien

t

Figure 12. Impact coefficients of upper-outer tube in south rib


50

40

30

20

10

00 25 50 75

Under impact

In normal service

Nor

mal

stre

ss: M

Pa

100

x coordinates of north longitudinal girder: m

125 150

Figure 13. Maximum normal stresses of north longitudinal girder




199

The modified arrangement of the hangers is described here.

Referring to Figure 6, hangers 1a to 17a and 1b9 and 17b9 are

provided with the smaller section of 13-7W5, while hangers 1b

to 17b and 1a9 to 17a9 are provided with the bigger section of

20-7W5. One may notice that this arrangement of the hangers is

symmetrical neither about the longitudinal centreline nor

about the transverse centreline. As the hangers of smaller

sections are more prone to fracture, in case one or both of the

smaller hangers carrying a transverse girder happen to

fracture, the remaining bigger hangers can still provide

effective support to the deck slab along a diagonal of the

transverse girder in plan (e.g. a line joining the anchorages of

hangers 5b and 5a9).

Table 3 shows six representative cases of hanger fracture that

may happen to the bridge of conventional and improved

hanger designs. The adjacent hangers most affected by the

fracture are identified and monitored for their maximum stress

increase. The factor of safety of a monitored hanger is then

calculated as the ratio of its tensile strength to the maximum

stress that occurs after fracture. As hangers in a group in the

conventional design have identical sections, the worst scenario

of simultaneous hanger fracture in a group is considered. The

fracture of the smaller hanger in the same anchorage of

improved design is considered for comparison with the

conventional hanger design.

Case 1 deals with fracture at anchorage 1 with the shortest

hangers, namely fracture of hangers 1a and 1b for conventional

design, and hanger 1a for improved design. Case 2 deals with

fracture at anchorage 5 with medium-length hangers, namely

fracture of hangers 5a and 5b for conventional design, and

hanger 5a for improved design. Case 3 deals with fracture at

anchorage 9 with the longest hangers, namely fracture of

hangers 9a and 9b for conventional design, and hanger 9a for

improved design. Case 4 deals with fracture at both anchorages

1 and 17 with the shortest hangers, namely fracture of hangers

1a, 1b, 17a and 17b for conventional design, and hangers 1a

50

40

30

20

10

00 25 50 75

Under impact

In normal service

Nor

mal

stre

ss: M

Pa

100

x coordinates of south longitudinal girder: m

125 150

Figure 14. Maximum normal stresses of south longitudinal girder


Case

Fractured hangers Monitored hangers Factor of safety

Conventional Improved Conventional Improved Conventional Improved Increase

1 1a, 1b 1a 2a 1b 3?13 3?84 22?7%

2 5a, 5b 5a 4b 5b 3?36 3?82 13?7%

3 9a, 9b 9a 8b, 10a 9b 3?53 3?84 8?7%

4 1a, 1b, 17a, 17b 1a, 17a 2a, 16b 16a 3?10 3?82 23?2%

5 5a, 5b, 13a, 13b 5a, 13a 4b, 14a 14a 3?29 3?79 13?2%

6 9a, 9b, 9a’, 9b’ 9a, 9b’ 8b, 10a, 8b’, 10a’ 10a, 8b’ 3?43 3?82 11?8%

Table 3. Factors of safety at most affected hangers for various

cases



200

and 17a for improved design. Case 5 deals with fracture at both

anchorage 5 and 13 with medium-length hangers, namely

fracture of hangers 5a, 5b, 13a and 13b for conventional

design, and hangers 5a and 13a for improved design. Case 6

deals with fracture at anchorage 9 with the longest hangers in

both ribs, namely fracture of hangers 9a, 9b, 9a9 and 9b9 for

conventional design, and hangers 9a and 9b9 for improved

design. The six cases are rather stringent tests of robustness as

many of them involve simultaneous fracture of more than one

hanger.

From the factors of safety shown in Table 3, one can draw

various conclusions. All the calculated factors of safety are well

above the minimum value of 2?0 for temporary situations

(MTPRC, 2007). The factors of safety of cases 4 to 6 are

slightly lower than those of cases 1 to 3, namely their

corresponding cases with half the number of fractured hangers.

Adopting the improved method of hanger design leads to

higher factors of safety compared to those of conventional

design. To a certain extent, this is caused by the use of 7-wire

strands having characteristic tensile strength of 11% higher

than that of prestressing steel wires in the original design.

Taking into account the characteristic tensile strength and

cross-sectional area of each hanger group, the improved

hanger group is only 7?6% stronger than the conventional

hanger group. Actually, the increases in factor of safety shown

350 Case 1Case 4

Case 2 Case 3Case 5 Case 6

Threshold300

250

200

100

150

50

00 30 60

Longitudinal girder coordinates: m

90 120 150

Nor

mal

stre

ss: M

Pa


for fracture of hangers of conventional design

120

100

80

60

40

20

140

Case 1 Case 2 Case 3

Case 6Case 4Threshold

Longitudinal girder coordinates: m

She

ar s

tress

: MP

a Case 5

01209060300 150

Figure 16. Maximum shear stresses of north longitudinal girder for

fracture of hangers of conventional design



201

in the last column of Table 3 are all above 7?6%. In addition,

one should bear in mind that the hangers monitored for the

conventional design are typically 8 m from the fractured

hangers, such that the impact effect is relatively insignificant.

In the improved hanger design, each hanger monitored has a

fractured hanger in the same group and hence the impact effect

is the most significant. One may therefore conclude that, when

sudden hanger fracture happens, the improved hanger design

can make the arch bridge safer and significant alteration of the

load path is more remote.

The effects of hanger fracture on the north longitudinal steel

girder are also assessed. Figures 15 and 16 show the maximum

normal stresses and maximum shear stresses, respectively, of

the north longitudinal steel girder for various cases of fracture

of hangers of the conventional design, while those for the

improved design are shown in Figures 17 and 18 respectively.

Figure 15 shows that, for all of the six representative cases of

hanger fracture, the normal stresses at the most affected parts

of longitudinal girder either approach or even exceed the

allowable normal stress of 210 MPa in accordance with the

140

120

100

80

60

40

20

She

ar s

tress

: MP

a

0

Longitudinal girder coordinates: m1209060300 150

Case 1 Case 2 Case 3

Case 6Case 4Threshold

Case 5

Figure 18. Maximum shear stresses of north longitudinal girder for

fracture of hangers of improved design

250

200

150

100

50

Nor

mal

stre

ss: M

Pa

0

Longitudinal girder coordinates: m1209060300 150

Case 1 Case 2 Case 3Case 6Case 4

ThresholdCase 5


for fracture of hangers of improved design



202

relevant design code (MOHURD, 2003), if the hangers have

been designed by the conventional method. Similarly,

Figure 16 shows that, for cases 1 and 4 of hanger fracture,

the allowable shear stress of 120 MPa is exceeded at certain

parts adjacent to the fractured hangers. To sum up, if the

hangers have been designed by the conventional method,

simultaneous fracture of both hangers in a group is a real

threat that must be considered, and the resulting alteration of

load path does affect the stresses in the longitudinal girders. If

any part of the longitudinal girders happens to fail because of

the resulting overstressing, progressive failure may be trig-

gered. Figures 17 and 18 show that, when hanger fracture

happens to the bridge with the improved hanger design, the

maximum normal stresses and maximum shear stresses of the

longitudinal girder are well below the respective allowable

values. This means that the longitudinal girders still have

sufficient safety margin against possible progressive failure

triggered by hanger fracture if the improved hanger design has

been adopted in the bridge.

From the comparison described in this section, it can be

concluded that, when the conventional design method is

adopted for the double-hanger anchorages in the through-

arch bridge, the bridge may be damaged by occasional local

fracture of hangers. However, if the improved hanger design

method is adopted, the bridge will still remain safe in case an

occasional local fracture of hangers happens. The bridge still

maintains a reasonable load-carrying capacity during an

appropriate length of time to allow the necessary emergency

measures to be taken.

7. Conclusions

The conventional design of double-hanger anchorages for

through-arch bridges is reviewed from the structural robust-

ness point of view. However, it is considered to improve neither

the safety of the bridge nor the convenience of hanger

replacement, since the identical hangers at an anchorage may

fracture simultaneously and possibly induce progressive fail-

ure. An improved hanger design method involving the use of

unequal hangers in a group with unequal initial stresses

adjusted by proper jacking during erection is therefore put

forward for better robustness. Finite-element models for an

authentic through-arch bridge have been built up for dynamic

analyses to evaluate the impact effects due to hanger fracture.

It is found that the hangers and the parts of the longitudinal

girder in the vicinity of the fractured hangers will experience

the highest impact effects, while components further away are

hardly affected. Although the smaller hanger in a group is

expected to fail first, the hanger arrangement in the improved

hanger design helps to preserve the load path of the structural

system, and thereby helps to maintain the robustness of the

bridge.

AcknowledgementsThe present work is partly supported by the Independent

Innovation Foundation of Shandong University, and the Small

Project Funding and the HKU SPACE Research Fund of The

University of Hong Kong, for which the authors are most grateful.

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